To be fair, but for a sign specifically advising when the box office would be opening, there really isn't something you would be able to see when you walked by the theatre in advance that would give you some indication of how soon the BO is in fact opening. The marquee is now up so that is a step in the right direction, but price scale signs typically don't go up until the day of the BO opening or sometimes late in the week before. So the fact that it "didn't look like they were remotely close to opening" doesn't really mean much. They could have been opening the BO today and it would have looked much the same.
Many may know this already, but at the risk of repetition, the minimum amount of time prior to first preview that the BO opens is actually a union contract-defined standard (Local 751). Some box offices open long before that, but there is a minimum which is based on a calculation involving the number of weeks that the show is on sale by phone/internet prior to first preview (basically, divide by 5, round up and add one).
So "American Idiot"'s first preview is announced for March 24. They went on sale via Amex email I believe on 1/27 (or was it 1/20), so that's eight (or nine) weeks of phone/internet sales before first preview. Divide by 5 and round up = 2 + 1 = 3. Which in theory would mean the BO should open no later than March 1.
"No matter how much you want the part, never let 'em see you sweat." -- Old Dry Idea commercial